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Simplifying x4 + -32x2 + 32 = 0 Reorder the terms: 32 + -32x2 + x4 = 0 Solving 32 + -32x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -32x2 + -32 + x4 = 0 + -32 Reorder the terms: 32 + -32 + -32x2 + x4 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -32x2 + x4 = 0 + -32 -32x2 + x4 = 0 + -32 Combine like terms: 0 + -32 = -32 -32x2 + x4 = -32 The x term is -32x2. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x2 + 256 + x4 = -32 + 256 Reorder the terms: 256 + -32x2 + x4 = -32 + 256 Combine like terms: -32 + 256 = 224 256 + -32x2 + x4 = 224 Factor a perfect square on the left side: (x2 + -16)(x2 + -16) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (x2 + -16) equal to 14.966629547 and -14.966629547.Subproblem 1
x2 + -16 = 14.966629547 Simplifying x2 + -16 = 14.966629547 Reorder the terms: -16 + x2 = 14.966629547 Solving -16 + x2 = 14.966629547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x2 = 14.966629547 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = 14.966629547 + 16 x2 = 14.966629547 + 16 Combine like terms: 14.966629547 + 16 = 30.966629547 x2 = 30.966629547 Simplifying x2 = 30.966629547 Take the square root of each side: x = {-5.564766801, 5.564766801}Subproblem 2
x2 + -16 = -14.966629547 Simplifying x2 + -16 = -14.966629547 Reorder the terms: -16 + x2 = -14.966629547 Solving -16 + x2 = -14.966629547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x2 = -14.966629547 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = -14.966629547 + 16 x2 = -14.966629547 + 16 Combine like terms: -14.966629547 + 16 = 1.033370453 x2 = 1.033370453 Simplifying x2 = 1.033370453 Take the square root of each side: x = {-1.016548303, 1.016548303}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.564766801, 5.564766801, -1.016548303, 1.016548303}
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